Chapter 9, Problem 33SE

w that in any group of $mn+1$people there is either a list of $m+1$people where a person in the list (except for the first person listed) is a descendant of the previous person on the list, or there are $n+1$people such that none of these people is a descendant of any of the othernpeople. [Hint:Use Exercise

32.]Suppose that (S, $\preccurlyeq$) is a well-founded partially ordered set. Theprinciple of well-founded inductionstates that P(x) is ue for all $x\in S$if $\forall x\left(\forall y\left(y\prec x\to P\left(y\right)\right)\to P\left(x\right)\right)$.